R=800x-0.25x^2

Solution for R=800x-0.25x^2 equation:

=800R-0.25R^2

We move all terms to the left:

-(800R-0.25R^2)=0

We get rid of parentheses

0.25R^2-800R=0

a = 0.25; b = -800; c = 0;
Δ = b2-4ac
Δ = -8002-4·0.25·0
Δ = 640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{640000}=800$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-800}{2*0.25}=\frac{0}{0.5}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+800}{2*0.25}=\frac{1600}{0.5}
=3200
$